Question

Solve: 12 Superscript x squared 5 x minus 4 Baseline = 12 Superscript 2 x 6 x = 2 x = –5 x = 2, x = –5 no solution.

Answer 1

The solutions to the problem are 2 and -5.

Given to us

$12^{x^2+5x-4}= 12^{2x+6}$

To find

the value of x.

Solution

$12^{x^2+5x-4}= 12^{2x+6}$

as the base on both, the sides are the same, therefore, equating the powers to each other.

${x^2+5x-4}= {2x+6}\\x^2 + 5x-2x-4-6=0\\x^2 + 5x-2x-10=0\\x(x+5)-2(x+5)=0\\(x-2)(x+5) = 0$

we got the two factors.

Now equating both the factors against 0,

$(x-2) =0\\x=2$

$(x+5)=0\\x=-5$

Therefore, the solutions to the problem are 2 and -5.

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